Large language models (LLMs) with enormous pre-training tokens and parameters emerge diverse abilities, including math reasoning, codegeneration, and instruction following. These abilities are further enhanced by supervised fine-tuning (SFT). While the open-source community has explored ad-hoc SFT for enhancing individual capabilities, proprietary LLMs exhibit versatility across various skills. Therefore, understanding the facilitation of multiple abilities via SFT is paramount. In this study, we specificially focuses on the interplay of data composition between mathematical reasoning, code generation, and general human-aligning abilities during SFT. We propose four intriguing research questions to explore the association between model performance and various factors including data amount, composition ratio, model size and SFT strategies. Our experiments reveal that distinct capabilities scale differently and larger models generally show superior performance with same amount of data. Mathematical reasoning and code generation consistently improve with increasing data amount, whereas general abilities plateau after roughly a thousand samples. Moreover, we observe data composition appears to enhance various abilities under limited data conditions, yet can lead to performance conflicts when data is plentiful. Our findings also suggest the amount of composition data influences performance more than the composition ratio. In analysis of SFT strategies, we find that sequentially learning multiple skills risks catastrophic forgetting. Our proposed Dual-stage Mixed Fine-tuning (DMT) strategy offers a promising solution to learn multiple abilities with different scaling patterns.

In math reasoning with large language models (LLMs), fine-tuning data augmentation by query evolution and diverse reasoning paths is empirically verified effective, profoundly narrowing the gap between open-sourced LLMs and cutting-edge proprietary LLMs. In this paper, we conduct an investigation for such data augmentation in math reasoning and are intended to answer: (1) What strategies of data augmentation are more effective; (2) What is the scaling relationship between the amount of augmented data and model performance; and (3) Can data augmentation incentivize generalization to out-of-domain mathematical reasoning tasks?To this end, we create two new dataset AugGSM8K and AugMATH, by complicating and diversifying the queries and sampling multiple reasoning paths from GSM8K and MATH.We obtained a series of LLMs called MuggleMath by fine-tuning LLaMA models on AugGSM8K and AugMATH. MuggleMath substantially achieves new state-of-the-art on GSM8K and MATH.A log-linear relationship and a segmented log-linear are presented between MuggleMath’s performance and the amount of augmented data on GSM8K and MATH, respectively.We also find that it is weak in out-of-domain math reasoning generalization from AugGSM8K to MATH and from AugMATH to GSM8K, which suggests that augmenting queries that cover a broader range of subjects is more beneficial for generalization.